Is there any way to get a specific angle using the knife tool?
This is a work around.
For a simple object like your cylinder, simply rotate it in object mode 35°, make the cut, then rotate the object back.


For more complex objects where you can not rotate it. You can align the view to a rotated face. You could duplicate a face out of your mesh and separate it in to a new object, or just add a new object, a plane or an empty; then align the view to it with  with ShiftNumPad 7.



Finally do not forget that you can roll the view, but that is limited to 15° increments.